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3 years ago

Find the number of sides of the regular polygon when the measure of an exterior angle is given.

1 answer:

8 0

$1.\\exterior\angle=30^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -30^\circ=150^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 150^\circ=180^\circ-\frac{360^\circ}{n}\\ -30^\circ=-\frac{360^\circ}{n}\ |*n\\ -30^\circ\ *n=-360^\circ \ |:-30^\circ\\ n=12\\\\ Number\ of\ sides\ is\ 12.$ $2.\\exterior\angle=10^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -10^\circ=170^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 170^\circ=180^\circ-\frac{360^\circ}{n}\\ -10^\circ=-\frac{360^\circ}{n}\ |*n\\ -10^\circ\ *n=-360^\circ \ |:-10^\circ\\ n=36\\\\ Number\ of\ sides\ is\ 36.$

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The sum of two integers is 26. the sum of the squares of the two integers is 340. what is the product of the two numbers?

Phoenix [80]

Lets say that the two unknown integers are $n$ and $m$ .

We know the following things about $n$ and $m$ :

$n+m=26$
$n^2+m^2=340$

And, we want to find $nm$ .

To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:

$(n+m)^2=n^2+2nm+m^2$

So, given what we know about the unknown integers, the previous can be written as:

$(26)^2=340+2nm$

We can easily solve for $nm$ :

$nm= \frac{(26)^2-340}{2}= \frac{676-340}{2}= \frac{336}{2}=168$

The answer is 168.

Another approach to solve the problem is, from the two starting equations, compute the values of $n$ and $m$ , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.

5 0

2 years ago

What is the value 24/25 ÷ 4/5 6th grade work.

Anna [14]

Answer:

as a decimal 0.048 and as a fraction 6/125

Step-by-step explanation:

Hope this helps :)

4 0

2 years ago

Estion

dalvyx [7]

Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:

$\mu = 15 \times \frac{45}{120} = 5.625$

The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

In which:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004$

$P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02$

$P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057$

$P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107$

$P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150$

$P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169$

Then:

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507$

0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ1

3 0

1 year ago

A population of crawfish in a section of the Louisiana bayou increased from 900,000 to 1.2 million between 2010 and 2011. If the

slega [8]

Answer: 1,599,960

Step-by-step explanation:

Since the population of crawfish in a section of the Louisiana bayou increased from 900,000 to 1.2 million between 2010 and 2011. The percentage increase in population will be:

= (1.2 million - 900000) / 900000 × 100

= 300000/900000 × 100

= 33.33%

Since the population increases by the same percentage between 2011 and 2012, then the population in 2012 will be:

= (100% + 33.33%) × 1.2 million

= 133.33% × 1.2 million

= 1.3333 × 1.2 million

= 1,599,960

The population in 2012 is 1,599,960

5 0

2 years ago

Consider the system of linear equations −4x+2y=4 and 4x−y=−6. Which is different?

Alexandra [31]

Answer:

one is plus + and the other is mines -

Step-by-step explanation:

8 0

2 years ago